phys. stat. sol. (b) 214, 471 (1999)
Subject classification: 77.80.Bh; 77.84.Dy; S11.1
Manifestation of Incommensurate Phasein the Dielectric Properties of NH4HSeO4 Crystals
B. Andriyevsky (a), O. Myshchyshyn (a), Z. Czapla (b), and S. Dacko (b)
(a) Faculty of Physics, Ivan Franko State University, 8 Kyryla and Mefodiya Str.,290005 Lviv, Ukraine
(b) Institute of Experimental Physics, Wrocaw University, pl. M. Borna 9,PL-50-204, Poland
(Received January 4, 1999; in revised form May 14, 1999)
Temperature (220 to 280 K) and frequency (0.02 to 1000 kHz) dependences of the real (e0) andimaginary (e00) parts of the complex electric permittivity for the ferroelectric b-cut of NH4HSeO4crystal have been investigated. The analysis of the experimental results has shown that the effec-tive elastic stiffness coefficient Ceff of the crystal decreases about three to four times in the tem-perature range of 256 to 262 K when compared to the paraelectric phase. Small oscillations of thetemperature dependence of e(T) have been revealed in the temperature range of the incommensu-rate phase (252 to 265 K), which have been interpreted as break off in the continuous change ofthe wave vector of the crystal structure caused by numerous transitions between commensurateand incommensurate subphases.
Ferroelectric crystals NH4HSeO4 (AHSe) are characterized by an incommensurate (IC)phase existing in the range of 250 to 262 K under normal conditions . The dielectricproperties of these crystals were investigated earlier [1 to 5]. In all these studies a max-imum of e(T) at the phase transition into the ferroelectric (FE) phase (Tc = 250 K) wasreported, but no anomalies were observed at the transition from paraelectric to ICphase (Ti = 262 K). The existence of the IC phase was testified in a rather indirect waywith the aid of dielectric measurements: the approaching of temperature Tc to Ti wasobserved at increasing external electric field  or hydrostatic pressure  applied tothe crystal. The other anomalies of dielectric properties specific for the IC phase ofAHSe crystals, such as fine periodic structure of the dependences of e(T) and tan d(T)in (N(CH3)4)2ZnCl4 crystals , have not been revealed so far.
The aim of the present study is the detailed investigation of the dielectric propertiesof AHSe crystal at different frequencies of the measuring electric field in the tempera-ture range of 220 to 280 K, including paraelectric (PE), IC and FE phases.
The b-cut sample of AHSe crystal (4.0 1.6 5.5 mm3) was prepared for measuring itsdielectric properties along the direction of spontaneous polarization. Gold electrodeswere evaporated on the b-faces. To avoid any influence of atmospheric humidity on thecrystal properties it was placed in a vacuum chamber (p = 104 Pa) on a copper platecooled by nitrogen gas. Under these conditions, the sample was mechanically free. The
B. Andriyevsky et al.: Manifestation of Incommensurate Phase in the Dielectric Properties 471
temperature in the chamber and the rate of its lowering in the range of 280 to 220 Kwere controlled automatically with an accuracy not worse than 5 103 K. The preci-sion LCR-meter HP 4284A connected with a personal computer was used for dielectricmeasurements. All the discussed results were obtained at frequencies 0.02, 0.2, 0.3, 0.4,0.5, 0.6, 0.8, 1, 3, 5, 8, 10, 12, 15, 20, 50, 80, 100, 120, 150, 200, 250, 300, 400, 500, 600,670, 800, 960, 1000 kHz under a measuring field of 3 V/cm.
3. Results and Discussion
Experimental investigations of AHSe crystals at different frequencies have revealed acomplicated structure of the temperature dependences of the real e0T and imaginarye00T parts of the complex electric permittivity (Figs. 1, 2). The temperature dependencesof e0T for different frequencies in the range of 0.5 to 50 kHz are similar. The maximummagnitude of e0 is practically unchanged under increasing frequency (Fig. 1), but the mag-nitude of e00 increases (Fig. 2). The e0T dependences in the temperature range 240 to 260K for frequencies 1 to 100 kHz are characterized predominantly by a single broad maxi-mum. The corresponding temperature dependences of e00 are characterized by a more com-plicated structure in the frequency range of 100 to 670 kHz with two or more extrema.This is caused by the fact that the effects of resonance interaction of the measuring elec-tric field and eigenvibrations of a sample take place just in this frequency range.
It is known that the thermodynamical analysis of proper ferroelectrics with the ICphase predicts a local minimum in the temperature dependence of the electric permit-tivity near the temperature of the transition into the FE phase . This conclusion isconfirmed for AHSe crystals, for which a tendency to a minimum near Tc = 250 K isseen on the temperature dependences of e0, and a clear minimum in the range of 238 to250 K is observed in the temperature dependences of e00 (Fig. 1, 2). The position of thee00T maximum near T = 250 to 253 K does not depend upon frequency, but the posi-tion of another neighboring one is shifted from the range T = 230 to 240 K at low
472 B. Andriyevsky, O. Myshchyshyn, Z. Czapla, and S. Dacko
Fig. 1. Temperature dependences of the real part of the electric permittivity e0bT of the AHSecrystal for the frequencies f = 1 kHz, 10 kHz, 0.1 MHz and 1 MHz of the measuring electric fieldalong the b-axes at cooling run of 0.91 K/min
f < 100 kHz) and high (f > 200 kHz) frequencies to the vicinity of T = 245 K at thefrequency f = 120 kHz. The latter frequency is close to the resonance one at T = 245 K.In this connection the mentioned shift of the low-temperature maximum of e00T dis-plays a nonlinearity of e00 related to the electric and mechanical action on the samplewhen approaching the resonance frequency. This experimental fact can be associatedwith a similar result obtained in , in which Tc approaches the almost unchangedvalue of Ti at increasing electric field and disappearing IC phase under fieldsE > 14 kV/cm (the so-called transition into the Lifshitz point).
Manifestation of Incommensurate Phase in the Dielectric Properties of NH4HSeO4 Crystals 473
Fig. 2. Temperature dependences of the imaginary part of the electric permittivity e00bT of theAHSe crystal for the frequencies f = 1 kHz, 10 kHz, 0.1 MHz and 1 MHz of measuring electricfield along the b-axes at cooling run of 0.91 K/min
Fig. 3. Temperature dependences of the real (e0) and imaginary (e00 parts of the electric permittiv-ity of the AHSe crystal for the frequency of 1 MHz at cooling run of 0.17 K/min
An interesting peculiarity of the temperature dependences of e0T and e00T at thefrequency of 1 MHz is its periodic behavior in the temperature range of 255 to 265 K(Fig. 3). At first view, a possible explanation of this fact can be a modulated solitonsuperstructure known in the IC phases . But the detailed analysis shows that thepositions of these extrema are different for different frequencies of the measuring elec-tric field. This testifies the resonance character of the observed periodic structure,which can be classified as the manifestation of resonance sequences at the formation ofstanding waves which fit in the sample of thickness l due to the fast temperaturechange in the elastic stiffness coefficient C of the crystal in the IC phase. For this casethe known relation takes place between the sample thickness l, the wavelength l, thevelocity V of acoustic waves, the resonance frequency fR, the elastic stiffness coefficientC, and the density r,
l n l2 n V
where n 1; 2; 3 . . . . Neglecting the temperature dependences of the length l and den-sity r of a sample, one can obtain the following condition for the observation ofthe row of vibration resonances with different numbers n at a given frequency(fR 1 MHz):
CT 4l2r f 2Rn2
: 2Substituting the known values l, r and fR 1 MHz into the formula (2), one can derivethe relation between the values C and n. The analysis of the frequency dependences ofe0 and e00 testifies that, at T 261:5 K, the main resonance frequency (n = 1) of thesample is equal to fR 250 kHz. Therefore, the maximum of the dependence e00T atT 261.5 K for the frequency 1 MHz in Fig. 3 corresponds to n = 4. In such a case thenumbers of the other maxima on this dependence can be determined uniquely, thuspermitting to calculate the dependence C(n) with the aid of formula (2) and to obtain
474 B. Andriyevsky, O. Myshchyshyn, Z. Czapla, and S. Dacko
Fig. 4. Temperature dependence of the elastic stiffness coefficient C of the AHSe crystal calculatedfrom the data of Fig. 3 and formula (2)
the corresponding dependence of C(T). The result of the calculations is presented inFig. 4. The presence of several extrema on the e0T and e00T dependences in a nar-row temperature range for 1 MHz is explained by a considerable temperature depen-dence of the elastic stiffness coefficient C(T).
The AHSe crystal is piezoelectric in the whole temperature range studied, so thatresonance-like regions in the frequency dependences e0 and e00 are expected. Since thesymmetry of the PE phase of AHSe (point symmetry group 2) allows different non-zero components of the piezoelectric tensor (d21, d22, d23 and d25) for the chosenb-direction of the measuring electric field, then several maxima in the e0f and e00f dependences are expected, corresponding to different vibrational resonances (see for-mula (1)), with different components of the elastic stiffness tensor C(a) and differentgeometric dimensions of the sample (4.0 1.6 5.5 mm3). The complexity of thesespectra can be also explained by the interaction of vibrational modes caused by theconside